List of practice Questions

2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is

What was distinctive about Eco’s academic writing style?

A closely wound solenoid of \(2000 \) turns and area of cross-section \(1.6 × 10^{-4}\  m^2\), carrying a current of \(4.0 \ A\), is suspended through its centre allowing it to turn in a horizontal plane. 
(a) What is the magnetic moment associated with the solenoid?
(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of \(7.5 × 10^{-2}\  T\) is set up at an angle of \(30º\) with the axis of the solenoid?

If \(3x^2-2ax+(a^2+2b^2+2c^2) = 2(ab+bc),\) then a,b,c can be in

Velocity of sound in vacuum is

If $f(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}}$ , then $f'(2) $ is equal to

In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only ?

In a library, the ratio of fiction books to non-fiction books is 7:5. The ratio of English fiction books to Hindi fiction books is 2:3. If there are 420 English fiction books, find the total number of non-fiction books in the library.

The average weight of a group of people increases by 2 kg when a person weighing 65 kg joins them. If the initial average weight of the group was 55 kg, find the ratio of the number of people initially in the group to the total number of people in the new group.

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is n(n+1). If the nth term of the progression is divisible by 7, then the smallest possible value of n is:

Two buses start simultaneously from the same place towards a destination which is 180 km away. The first bus travels at a speed of 40 km/h and the second bus travels at a speed of 60 km/h. The second bus reaches the destination, waits for some time and returns back. If the buses cross each other 90 km away from the starting point, then for how long did the second bus wait at the destination?

From the given information, calculate enthalpy of formation of 2 moles of $C_6H_6$(l) at 25°C. Given: $CH(C_6H_6$(l)) = –3264.6 kJ/mol $CH(C(s))$ = –393.5 kJ/mol $fH(H_2O(l))$ = –285.83 kJ/mol

Find out value of $C_p/C_y$ for an ideal gas undergoing reversible adiabatic process for which $P ∝ T^3$ is given

Which of the following is true regarding coagulation of egg:

Find out E cell of the given cell M | M²⁺ | | x^2-|x.|
Eº_M²⁺_{I M} = 0.34 V
E°_x|x^2- = 0.46 V

Find out the shortest wavelength of paschen series for H- atom

Which of the following d-block elements has maximum unpaired electron in ground state electronic configuration?

Match the column.

Column-I (Compounds)		Column-II (Configurations)
A.	TiCl4	(1)	e3t23
B.	FeO42-	(2)	e2t20
C.	FeCl42-	(3)	e2t23
D.	MnCl42-	(4)	e0t20

If y=\(\frac{2\cos2\theta+\cos\theta}{\cos3\theta+\cos^2\theta+\cos\theta}\), Then value of y''+y'+y is

A line L is perpendicular to y = 2x + 10 such that it touches the parabola y² = 4(x – g). Then the distance between point of contact and origin is equal to

A=\(\begin{bmatrix}   \alpha & \alpha & \alpha \\   \beta & \alpha & -\beta \\   -\alpha & \alpha & \alpha  \end{bmatrix}\)B is formed by co-factor of A matrix, then find out determinant of AB.

If |a| = 2, |b| = 3 and a = b × 2, then minimum value of \(|\hat{c} - a|^2\) is:

Area bounded by y = -2|x| and y = x|x| is:

Let image of point(8,5,7) with respect to line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}\) is (α,β,γ). Then, α+β+γ is equal to______.

\(\left( \frac{3^{\frac{1}{5}}}{x}+\frac{2x}{5^\frac{1}{3}} \right)^{12}\)Find which term is constant.